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Register a new userObjective Estimation of Spatially Variable Parameters of Epidemic Type Aftershock Sequence Model: Application to California
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The ETAS model is widely employed to model the spatio-temporal distribution of earthquakes, generally using spatially invariant parameters. We propose an efficient method for the estimation of spatially varying parameters, using the Expectation-Maximization (EM) algorithm and spatial Voronoi tessellation ensembles. We use the Bayesian Information Criterion (BIC) to rank inverted models given their likelihood and complexity and select the best models to finally compute an ensemble model at any location. Using a synthetic catalog, we also check that the proposed method correctly inverts the known parameters. We apply the proposed method to earthquakes included in the ANSS catalog that occurred within the time period 1981-2015 in a spatial polygon around California. The results indicate a significant spatial variation of the ETAS parameters. We find that the efficiency of earthquakes to trigger future ones (quantified by the branching ratio) positively correlates with surface heat flow. In contrast, the rate of earthquakes triggered by far-field tectonic loading or background seismicity rate shows no such correlation, suggesting the relevance of triggering possibly through fluid-induced activation. Furthermore, the branching ratio and background seismicity rate are found to be uncorrelated with hypocentral depths, indicating that the seismic coupling remains invariant of hypocentral depths in the study region. Additionally, triggering seems to be mostly dominated by small earthquakes. Consequently, the static stress change studies should not only focus on the Coulomb stress changes caused by specific moderate to large earthquakes but also account for the secondary static stress changes caused by smaller earthquakes.
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We investigate the possibility to extract information contained in seismic waveforms propagating in fluid-filled porous media by developing and using a full waveform inversion procedure valid for layered structures. To reach this objective, we first solve the forward problem by implementing the Biot theory in a reflectivity-type simulation program. We then study the sensitivity of the seismic response of stratified media to the poroelastic parameters. Our numerical tests indicate that the porosity and consolidation parameter are the most sensitive parameters in forward and inverse modeling, whereas the permeability has only a very limited influence on the seismic response. Next, the analytical expressions of the sensitivity operators are introduced in a generalized least-square inversion algorithm based on an iterative modeling of the seismic waveforms. The application of this inversion procedure to synthetic data shows that the porosity as well as the fluid and solid parameters can be correctly reconstructed as long as the other parameters are well known. However, the strong seismic coupling between some of the model parameters makes it difficult to fully characterize the medium by a multi-parameter inversion scheme. One solution to circumvent this difficulty is to combine several model parameters according to rock physics laws to invert for composite parameters. Another possibility is to invert the seismic data for the perturbations of the medium properties, such as those resulting from a gas injection.
The aftershock productivity law, first described by Utsu in 1970, is an exponential function of the form K=K0.exp({alpha}M) where K is the number of aftershocks, M the mainshock magnitude, and {alpha} the productivity parameter. The Utsu law remains empirical in nature although it has also been retrieved in static stress simulations. Here, we explain this law based on Solid Seismicity, a geometrical theory of seismicity where seismicity patterns are described by mathematical expressions obtained from geometric operations on a permanent static stress field. We recover the exponential form but with a break in scaling predicted between small and large magnitudes M, with {alpha}=1.5ln(10) and ln(10), respectively, in agreement with results from previous static stress simulations. We suggest that the lack of break in scaling observed in seismicity catalogues (with {alpha}=ln(10)) could be an artefact from existing aftershock selection methods, which assume a continuous behavior over the full magnitude range. While the possibility for such an artefact is verified in simulations, the existence of the theoretical kink remains to be proven.
In this paper we propose a novel SEIR stochastic epidemic model. A distinguishing feature of this new model is that it allows us to consider a set up under general latency and infectious period distributions. To some extent, queuing systems with infinitely many servers and a Markov chain with time-varying transition rate are the very technical underpinning of the paper. Although more general, the Markov chain is as tractable as previous models for exponentially distributed latency and infection periods. It is also significantly simpler and more tractable than semi-Markov models with a similar level of generality. Based on the notion of stochastic stability, we derive a sufficient condition for a shrinking epidemic in terms of the queuing systems occupation rate that drives the dynamics. Relying on this condition, we propose a class of ad-hoc stabilising mitigation strategies that seek to keep a balanced occupation rate after a prescribed mitigation-free period. We validate the approach in the light of recent data on the COVID-19 epidemic and assess the effect of different stabilising strategies. The results suggest that it is possible to curb the epidemic with various occupation rate levels, as long as the mitigation is not excessively procrastinated.
29 August 2018: Artificial intelligence nails predictions of earthquake aftershocks. This Nature News headline is based on the results of DeVries et al. (2018) who forecasted the spatial distribution of aftershocks using Deep Learning (DL) and static stress feature engineering. Using receiver operating characteristic (ROC) curves and the area under the curve (AUC) metric, the authors found that a deep neural network (DNN) yields AUC = 0.85 compared to AUC = 0.58 for classical Coulomb stress. They further showed that this result was physically interpretable, with various stress metrics (e.g. sum of absolute stress components, maximum shear stress, von Mises yield criterion) explaining most of the DNN result. We here clarify that AUC c. 0.85 had already been obtained using ROC curves for the same scalar metrics and by the same authors in 2017. This suggests that DL - in fact - does not improve prediction compared to simpler baseline models. We reformulate the 2017 results in probabilistic terms using logistic regression (i.e., one neural network node) and obtain AUC = 0.85 using 2 free parameters versus the 13,451 parameters used by DeVries et al. (2018). We further show that measured distance and mainshock average slip can be used instead of stress, yielding an improved AUC = 0.86, again with a simple logistic regression. This demonstrates that the proposed DNN so far does not provide any new insight (predictive or inferential) in this domain.
We investigate the relationship between synoptic/local meteorological patterns and PM10 air pollution levels in the metropolitan area of Naples, Italy. We found that severe air pollution crises occurred when the 850 and 500 hpa geopotential heights and their relative temperatures present maximum values above the city. The most relevant synoptic parameter was the 850 hPa geopotential height, which is located about 1500 m of altitude. We compared local meteorological conditions (specifically wind stress, rain amount and thermal inversion) against the urban air pollution levels from 2009 to 2013. We found several empirical criteria for forecasting high daily PM10 air pollution levels in Naples. Pollution crises occurred when (a) the wind stress was between 1 and 2 m/s, (b) the thermal inversion between two strategic locations was at least 3{deg}C/200m and (c) it did not significantly rain for at least 7 days. Beside these meteorological conditions, severe pollution crises occurred also during festivals when fireworks and bonfires are lighted, and during anomalous breeze conditions and severe fire accidents. Finally, we propose a basic model to predict PM10 concentration levels from local meteorological conditions that can be easily forecast a few days in advance. The synthetic PM10 record predicted by the model was found to correlate with the PM10 observations with a correlation coefficient close to 0.80 with a confidence greater than 99%. The proposed model is expected to provide reliable information to city officials to carry out practical strategies to mitigate air pollution effects. Although the proposed model equation is calibrated on the topographical and meteorological conditions of Naples, it should be easily adaptable to alternative locations.
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